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# If x, y and z are positive numbers, is x/y > (x + z)/(y + z) ?

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Math Expert
Joined: 02 Sep 2009
Posts: 51215
If x, y and z are positive numbers, is x/y > (x + z)/(y + z) ?  [#permalink]

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26 Nov 2018, 00:25
00:00

Difficulty:

55% (hard)

Question Stats:

60% (01:19) correct 40% (01:42) wrong based on 43 sessions

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If x, y and z are positive numbers, is $$\frac{x}{y} > \frac{x + z}{y + z}$$ ?

(1) x > z

(2) x > y

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Joined: 19 Nov 2017
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Location: India
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Re: If x, y and z are positive numbers, is x/y > (x + z)/(y + z) ?  [#permalink]

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26 Nov 2018, 00:39
Bunuel wrote:
If x, y and z are positive numbers, is $$\frac{x}{y} > \frac{x + z}{y + z}$$ ?

(1) x > z

(2) x > y

$$\frac{x}{y} > \frac{x + z}{y + z}$$
Cross multiplying
xy + xz > xy + yz
xy + xz > xy + yz
x>y

Hence, B
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Re: If x, y and z are positive numbers, is x/y > (x + z)/(y + z) ?  [#permalink]

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26 Nov 2018, 17:34
Bunuel wrote:
If x, y and z are positive numbers, is $$\frac{x}{y} > \frac{x + z}{y + z}$$ ?

(1) x > z

(2) x > y

From given eqn we can deduce the following:
xy+xz>xy+yz
z(x-y)>0--(A)

so using 1: x>z , we are not given any relation about y so in -sufficient

From 1: X>Y
for any value of X >Y value the equation ( A) would stand true so B is sufficient..
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Re: If x, y and z are positive numbers, is x/y > (x + z)/(y + z) ? &nbs [#permalink] 26 Nov 2018, 17:34
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